The project also had had a tangible demonstration impact.
Is the above sentence grammatically correct? The event occurred a few years ago.
It would be grammatical in the right context. 'had had' is past perfect, referring to the past of the past, or something that happened earlier than a past tense context. A suitable past tense context could be:
Last year, the director requested an increase of funding. She said the research had begun to yield interesting results. The project also had had a tangible demonstration impact.
italics = past tense, time -x, bold = past perfect, time -x-y